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1.
Ikuo Yoneda 《Archive for Mathematical Logic》2003,42(5):423-433
We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable
CM-trivial with weak elimination of imaginaries.
Received: 21 December 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03C45
Key words or phrases: CM-triviality – Generic structures – Stability 相似文献
2.
The Belavkin equation, describing the continuous measurement of the position of a quantum particle, is studied. A rigorous
representation of its solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on
the complex Cameron-Martin space is given.
Received: 7 January 2002 / Revised version: 20 June 2002 / Published online: 19 December 2002
Mathematics Subject Classification (2000): 81, 81S40, 60H15
Key words or phrases: Belavkin equation – Continuous measurement – Quantum theory – Oscillatory integrals – Feynman path integrals 相似文献
3.
This paper presents a renormalization and homogenization theory for fractional-in-space or in-time diffusion equations with
singular random initial conditions. The spectral representations for the solutions of these equations are provided. Gaussian
and non-Gaussian limiting distributions of the renormalized solutions of these equations are then described in terms of multiple
stochastic integral representations.
Received: 30 May 2000 / Revised version: 9 November 2001 / Published online: 10 September 2002
Mathematics Subject Classification (2000): Primary 62M40, 62M15; Secondary 60H05, 60G60
Key words or phrases: Fractional diffusion equation – Scaling laws – Renormalised solution – Long-range dependence – Non-Gaussian scenario – Mittag-Leffler
function – Stable distributions – Bessel potential – Riesz potential 相似文献
4.
Massoud Pourmahdian 《Archive for Mathematical Logic》2003,42(5):415-421
We prove that for any simple theory which is constructed via Fr?issé-Hrushovski method, if the forking independence is the
same as the d-independence then the stable forking property holds.
Received: 22 January 2001 /
Published online: 19 December 2002
This article is part of the author's D-Phil thesis, written at the University of Oxford and supported by the Ministry of
Higher Education of Iran. The author would like to thank the Institute for Studies in Theoretical Physics and Mathematics
(IPM), Tehran, Iran, for its financial support whilst working on this article.
Mathematics Subject Classification (2000): 03C45
Key words or phrases: Generic structures – Fr?issé-Hrushovski method – Predimension – Simple theories – Stable theories – Stable forking conjecture 相似文献
5.
Sara Negri 《Archive for Mathematical Logic》2003,42(4):389-401
Geometric theories are presented as contraction- and cut-free systems of sequent calculi with mathematical rules following
a prescribed rule-scheme that extends the scheme given in Negri and von Plato (1998). Examples include cut-free calculi for
Robinson arithmetic and real closed fields. As an immediate consequence of cut elimination, it is shown that if a geometric
implication is classically derivable from a geometric theory then it is intuitionistically derivable.
Received: 18 April 2001 /
Published online: 10 October 2002
Mathematics Subject Classification (2000): 03F05, 18C10, 18B15
Key words or phrases: Cut elimination – Geometric theories – Barr's theorem 相似文献
6.
We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined
in terms of games.
Received: 8 July 1999 Published online: 19 December 2002
RID="*"
ID="*" The author wishes to thank the Swiss National Science Foundation for supporting him.
The authors thank the referee for helpful comments.
Mathematics Subject Classification (2000): 03E02, 05D10, 03E35
Key words or phrases: Dual Ramsey Theorem – Dual Ellentuck Theorem – Partitions – Games 相似文献
7.
We introduce a new upper bound for the maximum-entropy sampling problem. Our bound is described as the solution of a linear
integer program. The bound depends on a partition of the underlying set of random variables. For the case in which each block
of the partition has bounded cardinality, we describe an efficient dynamic-programming algorithm to calculate the bound. For
the very special case in which the blocks have no more than two elements, we describe an efficient algorithm for calculating
the bound based on maximum-weight matching. This latter formulation has particular value for local-search procedures that
seek to find a good partition. We relate our bound to recent bounds of Hoffman, Lee and Williams. Finally, we report on the
results of some computational experiments.
Received: September 27, 2000 / Accepted: July 26, 2001 Published online: September 5, 2002
Key words. experimental design – design of experiments – entropy – maximum-entropy sampling – matching – integer program – spectral
bound – Fischer's inequality – branch-and-bound – dynamic programming
Mathematics Subject Classification (2000): 52B12, 90C10
Send offprint requests to: Jon Lee
Correspondence to: Jon Lee 相似文献
8.
Byeong-Kweon Oh 《Mathematische Zeitschrift》2003,244(2):399-413
In this article, we prove that there are only finitely many positive definite integral quadratic forms of rank n+3(n≥2) that represent all positive definite integral quadratic forms of rank n but finitely many exceptions. Furthermore we determine all diagonal quadratic forms having such property and its exceptions
remaining four as candidates.
Received: 29 November 2000 ; in final form: 8 August 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (2000): 11E12, 11E20. 相似文献
9.
We introduce a Gentzen-style sequent calculus axiomatization for Basic Predicate Calculus. Our new axiomatization is an improvement
of the previous axiomatizations, in the sense that it has the subformula property. In this system the cut rule is eliminated.
Received: 18 April 2000 / Published online: 2 September 2002
Mathematics Subject Classification (2000): Primary 03F05; Secondary 03F99, 03B60
Key words or phrases: Basic predicate calculus – Cut elimination – Sequent 相似文献
10.
Andrzej Rozkosz 《Probability Theory and Related Fields》2003,125(3):393-407
We extend the definition of solutions of backward stochastic differential equations to the case where the driving process
is a diffusion corresponding to symmetric uniformly elliptic divergence form operator. We show existence and uniqueness of
solutions of such equations under natural assumptions on the data and show its connections with solutions of semilinear parabolic
partial differential equations in Sobolev spaces.
Received: 22 January 2002 / Revised version: 10 September 2002 / Published online: 19 December 2002
Research supported by KBN Grant 0253 P03 2000 19.
Mathematics Subject Classification (2002): Primary 60H30; Secondary 35K55
Key words or phrases: Backward stochastic differential equation – Semilinear partial differential equation – Divergence form operator – Weak solution 相似文献
11.
Tadahisa Funaki 《Probability Theory and Related Fields》2003,126(2):155-183
We consider random evolution of an interface on a hard wall under periodic boundary conditions. The dynamics are governed
by a system of stochastic differential equations of Skorohod type, which is Langevin equation associated with massless Hamiltonian
added a strong repelling force for the interface to stay over the wall. We study its macroscopic behavior under a suitable
large scale space-time limit and derive a nonlinear partial differential equation, which describes the mean curvature motion
except for some anisotropy effects, with reflection at the wall. Such equation is characterized by an evolutionary variational
inequality.
Received: 10 January 2002 / Revised version: 18 August 2002 /
Published online: 15 April 2003
Mathematics Subject Classification (2000): 60K35, 82C24, 35K55, 35K85
Key words or phrases: Hydrodynamic limit – Effective interfaces – Hard wall – Skorohod's stochastic differential equation – Evolutionary variational
inequality 相似文献
12.
Arthur W. Apter 《Archive for Mathematical Logic》2002,41(8):705-719
We prove three theorems concerning Laver indestructibility, strong compactness, and measurability. We then state some related
open questions.
Received: 11 December 1999 / Revised version: 17 September 2000 / Published online: 2 September 2002
Mathematics Subject classification (2000): 03E35, 03E55
Keywords or phrases: Measurable cardinal – Strongly compact cardinal – Supercompact cardinal – Indestructibility 相似文献
13.
Sándor Jenei 《Archive for Mathematical Logic》2003,42(5):489-514
We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical
characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard
algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows
from their other axioms.
Received: 7 January 2002 / Revised version: 4 April 2002 /
Published online: 19 December 2002
RID="*"
ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782).
Mathematics Subject Classification (2000): 20M14, 06F05
Key words or phrases: Residuated lattice – Conjunction for non-classical logics 相似文献
14.
Nathalie Eisenbaum 《Probability Theory and Related Fields》2003,125(3):381-392
We show that fractional Brownian motions with index in (0,1] satisfy a remarkable property: their squares are infinitely
divisible. We also prove that a large class of Gaussian processes are sharing this property. This property then allows the
construction of two-parameters families of processes having the additivity property of the squared Bessel processes.
Received: 1 April 2002 / Revised version: 7 September 2002 / Published online: 19 December 2002
Mathematics Subject Classification (2000): 60E07, 60G15, 60J25, 60J55
Key words or phrases: Gaussian processes – Infinite divisibility – Markov processes 相似文献
15.
Roberto Maieli 《Archive for Mathematical Logic》2003,42(3):205-220
We introduce a new correctness criterion for multiplicative non commutative proof nets which can be considered as the non-commutative
counterpart to the Danos-Regnier criterion for proof nets of linear logic. The main intuition relies on the fact that any
switching for a proof net (obtained by mutilating one premise of each disjunction link) can be naturally viewed as a series-parallel order variety (a cyclic relation) on the conclusions of the proof net.
Received: 8 November 2000 / Revised version: 21 June 2001 / Published online: 2 September 2002
Research supported by the EU TMR Research Programme ``Linear Logic and Theoretical Computer Science'.
Mathematics Subject Classification (2000): 03F03, 03F07, 03F52, 03B70
Key words or phrases: Linear and non-commutative logic – Proof nets – Series-parallel orders and order varieties 相似文献
16.
We consider the Max FS problem: For a given infeasible linear system A
x≤b, determine a feasible subsystem containing as many inequalities as possible. This problem, which is NP-hard and also difficult
to approximate, has a number of interesting applications in a wide range of fields. In this paper we examine structural and
algorithmic properties of Max FS and of Irreducible Infeasible Subsystems (IISs), which are intrinsically related since one must delete at least one constraint from each IIS to attain feasibility.
First we provide a new simplex decomposition characterization of IISs and prove that finding a smallest cardinality IIS is very difficult to approximate. Then we discuss
structural properties of IIS-hypergraphs, i.e., hypergraphs in which each edge corresponds to an IIS, and show that recognizing
IIS-hypergraphs subsumes the Steinitz problem for polytopes and hence is NP-hard. Finally we investigate rank facets of the
Feasible Subsystem polytope whose vertices are incidence vectors of feasible subsystems of a given infeasible system. In particular, using the IIS-hypergraph
structural result, we show that only two very specific types of rank inequalities induced by generalized antiwebs (which generalize
cliques, odd holes and antiholes to general independence systems) can arise as facets.
Received: December 2000 / Accepted: November 2002 Published online: February 14, 2003
RID="⋆"
ID="⋆" Part of this work was done while the first two authors were with the School of OR&IE, Cornell University, USA. A preliminary
version appeared in the Proceedings of the 10th IPCO conference [7], held in Graz, Austria, June 1999. This work was supported
by NSF grant DMS-9527124.
Key words. infeasible linear systems – feasible subsystems – Irreducible Infeasible Subsystem (IIS) – IIS-hypergraphs – independence
systems – feasible subsystem polytope – rank facets 相似文献
17.
Mirjana Borisavljević 《Archive for Mathematical Logic》2003,42(4):371-387
This paper presents a cut-elimination procedure for classical and intuitionistic logic, in which cut is eliminated directly,
without introducing the mix rule. The well-known problem of cut eliminations, when in the derivation the contractions of the
cut-formulae are above the premisses of the cut, will be solved by new transformations of the derivation.
Received: 1 June 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03F05
Key words or phrases: Systems of sequents – Cut-elimination theorem 相似文献
18.
In this paper, we describe how to reformulate a problem that has second-order cone and/or semidefiniteness constraints in
order to solve it using a general-purpose interior-point algorithm for nonlinear programming. The resulting problems are smooth
and convex, and numerical results from the DIMACS Implementation Challenge problems and SDPLib are provided.
Received: March 10, 2001 / Accepted: January 18, 2002 Published online: September 27, 2002
Key Words. semidefinite programming – second-order cone programming – interior-point methods – nonlinear programming
Mathematics Subject Classification (2000): 20E28, 20G40, 20C20 相似文献
19.
The purpose of this work is the study of the partition function of a -dimensional lattice directed polymer in a Gaussian random environment being the inverse of temperature). In the low-dimensional cases , we prove that for all , the renormalized partition function converges to 0 and the correlation of two independent configurations does not converge to 0. In the high dimensional case (), a lower tail of has been obtained for small . Furthermore, we express some thermodynamic quantities in terms of the path measure alone.
Received: 8 June 2001 / Revised version: 8 February 2002 / Published online: 22 August 2002
Mathematics Subject Classification (2000): 60K37, 82D30
Key words or phrases: Directed polymer in random environment – Gaussian environment – partition function 相似文献
20.
The stability number α(G) for a given graph G is the size of a maximum stable set in G. The Lovász theta number provides an upper bound on α(G) and can be computed in polynomial time as the optimal value of the Lovász semidefinite program. In this paper, we show that
restricting the matrix variable in the Lovász semidefinite program to be rank-one and rank-two, respectively, yields a pair
of continuous, nonlinear optimization problems each having the global optimal value α(G). We propose heuristics for obtaining large stable sets in G based on these new formulations and present computational results indicating the effectiveness of the heuristics.
Received: December 13, 2000 / Accepted: September 3, 2002 Published online: December 19, 2002
RID="★"
ID="★" Computational results reported in this paper were obtained on an SGI Origin2000 computer at Rice University acquired
in part with support from NSF Grant DMS-9872009.
Key Words. maximum stable set – maximum clique – minimum vertex cover – semidefinite program – semidefinite relaxation – continuous
optimization heuristics – nonlinear programming
Mathematics Subject Classification (2000): 90C06, 90C27, 90C30 相似文献